3.20. Combining Estimates from Several People

Applies to: @RISK 5.x–7.x

Several people gave me their assessments of the likely impact of a risk or a benefit, but naturally their estimates vary. Also, I have higher confidence in some opinions than others. How can I combine these assessments in @RISK?

We often say in ordinary language that we give more weight to one thing than another in making a decision, and it's the same in this situation. You want to set up a little table of weights and @RISK probability distributions, and the question then is how to give each distribution the appropriate weight. It would be easy to take the weighted average of the distributions, but that causes the extreme opinions to be under-represented. There are many possible approaches that don't have that problem, and the attached workbook shows four of them.

Sheet1 lets the contributors specify different distributions, not just different parameters to the same distribution. The weights are converted to percentages, and then using the number of iterations (which you specify) each distribution is sampled for the appropriate number of iterations.

Sheet1A is similar, and in fact it uses the exact same distributions as Sheet1. But it uses a RiskDiscrete function to sample the individual distributions in the appropriate proportions. This one does not need you to place the number of iterations in the workbook.

Sheet2 takes a different approach, computing weighted averages of the cumulative probabilities (the CDFs, not the PDFs. This could have been done with different distributions like Sheet1, but we also took the opportunity to show how you could set up a table of pessimistic, most likely, and optimistic cases and use the same distribution for all of them.

Sheet3 uses a multinomial distribution. Over the course of the simulation, each of the five distributions is samples in the appropriate proportion, based on the weights.

In all four cases, the combined function is wrapped in a RiskMakeInput function. That ensures that only the combined distribution, not the individual assessments, will show up in sensitivity graphs and figures. See also:All Articles about RiskMakeInput.